$g(n) = 6n^{2}-2(h(n))$ $h(x) = 3x^{2}-x-7$ $ h(g(-8)) = {?} $
Solution: First, let's solve for the value of the inner function, $g(-8)$ . Then we'll know what to plug into the outer function. $g(-8) = 6(-8)^{2}-2(h(-8))$ To solve for the value of $g$ , we need to solve for the value of $h(-8)$ $h(-8) = 3(-8)^{2}-(-8)-7$ $h(-8) = 193$ That means $g(-8) = 6(-8)^{2}+(-2)(193)$ $g(-8) = -2$ Now we know that $g(-8) = -2$ . Let's solve for $h(g(-8))$ , which is $h(-2)$ $h(-2) = 3(-2)^{2}-(-2)-7$ $h(-2) = 7$